Elementary math chat is a weekly math chat where participants come to discuss best practices, examine student work, explore routines for reasoning and research that guides and supports pedagogy centered on problem and student based learning.
Hi, everyone! I'm Annie, a sometimes K-5 math coach mostly based near Philly. I'm not in a school setting, so it's year round for me. This time of year, I love rhubarb and pokeweed. #ElemMathChat
Hi I am Melynee in OK I teach 6-8th grade Ss w/disabilities. Tomorrow is students last day of school. Teacher's last day is June 4 due to the teacher walk out Seasonal fruit please! #ElemMathChat
#elemmathchat I'm Kit in NYC teaching MS (but 6th grade only next year). I have 19 instructional days left.
My current favorite seasonal food is cherries!
I’m Mary, a first grade teacher from central California. With one day left in the classroom, my favorite seasonal food is anything I didn’t have to make myself. #elemmathchat
We are going to look at some student solutions to this problem and decide whether each students knows or doesn’t know each of those ideas (or if we don't have enough evidence to decide). #ElemMathChat
My name is Natalie. Math Coach Last day was today with kids but I still have contract days. PD with teachers, trying new things with kids. Etc. might fall asleep. Already horizontal. #elemmathchat
For each student and each idea, we’ll decide what they currently DO know about it, what they currently DON’T know, or that we can’t tell from the evidence. #ElemMathChat
A1: James knows how to find area and perimeter. He seems to struggle with determining the reasonableness of his answer. 27 x 28 are not reasonable dimensions for that rectangle. #elemmathchat
I’m planning on developing some mini pd lessons on number sense routines. I’m sure that will keep me going for a few weeks. I must have many irons in my fire at all time to feel right #ElemMathChat
A1: I think he knows opposite sides are equal and that’s about it. He knows the formulas. Can’t tell if he really understands perimeter and area. #elemmathchat
He just does some things with numbers. But after says something about multiplying to find area then he adds the four sides but doesn’t say why. Wondering if he just has gotten use to doing it. #elemmathchat
As a reminder, here's "the" solution to the problem - the small rectangles must have dimensions 9 and 12 to fit the picture (4 across the top, 3 across the bottom). #ElemMathChat
But do they seem reasonable if you're ignoring the small rectangles completely? I'm thinking you might be thinking about something he's not maybe? #ElemMathChat
A2: I would ask James how he determined that the length of the sides were 27 and 28. Then I would ask if there were any other possible dimensions for the rectangle. #elemmathchat
I am not 100% convinced he understands what perimeter means or how to reason with it, but I wouldn’t be surprised if he could find it given the l and w. Seems to know the formula well #elemmathchat
Yea, that's an interesting question. Does he understand congruence but doesn't see how it applies here? And does that mean there's something he doesn't understand about congruence? #elemmathchat
No problem. It happens when looking at student work (and not having thought about the problem for a couple of weeks). "Whoa! What are they doing again??" #ElemMathChat
I'm wondering why she decided to find the square root. If she was finding the square root she would be thinking of the area of a square. the shape isn't a square, which means she may also struggle with the concept of congruence. #elemmathchat
Yea...and we sure wonder why. To undo the "squared" exponent? Because she thinks it's a square? It's not unrelated to the problem, but... #ElemMathChat
A4: I would ask her why she decided to find the square root. I'd also inquire about her understanding of the difference between a square and a rectangle. #elemmathchat
So we might wonder if she DID think it was a square. Maybe she assumes the picture is not drawn to scale, or is ignoring the small rectangles, or...., or ....! #ElemMathChat
And how she answers the first question might impact how you ask the second. Maybe she was thinking about 756 units squared and not thinking shapes at all. Or maybe she was thinking rectangles and squares have the same "rule" for finding sides #elemmathchat
Sure. But that's why we're trying to figure out what we can and can't conclude from the work. We often end up with a lot of things in the "I can't tell!" pile, which is actually good. Keeps us from jumping to conclusions about what they do and don't know. #ElemMathChat
This is exactly why we need to provide feedback and investigate further as soon as possible. Waiting to check work prevents us from having a true understanding of what was done and why. #elemmathchat
#swdmathchat
I think math facts are important. But want to stress the efficiency, choice of strategy based on the numbers (flexibility) more than knowing by memory
A5 Matteo knows a formula I wonder if he read the problem wrong. If he did Does he know the properties of a rectangle? I see how he got his answer. I would ask him what is a perimeter? What is area. Can you give me a real world example of both? #ElemMathChat
Or puts people in the mode of sorting into "right" and "wrong" - these three kids don't all belong in the same "wrong" pile, for sure. Definitely critical to check in often. #ElemMathChat
This is exactly what we've been working on at my school. Diagnosing specific errors and misconceptions and reteaching to the specific error. If we want students to get to mastery, we can't only focus on right vs. wrong. #elemmathchat
A6: My first question for Matteo would be "does this make sense?" I'd want him to label the rectangle and see if his dimensions of 756 makes sense. #elemmathchat
A6 Matteo, can you give me a real world example of perimeter? How about area? What relationship do these two things have to one another? How does that relate to the formula you used? I want to ask him these things to get him thinking and evaluating his own work #ElemMathChat
And that "diagnosing" piece is SO important. We so often jump to "reteach" before we figure out what we should be reteaching (= waste of precious time). We love using #NoticeWonder stance to help us get better at diagnosing instead of assuming/judging. #ElemMathChat
Like Matteo! He might know a ton about how to solve the problem, but has a really specific bit of wrong information about what square units means. Maybe he doesn't need to be "re-taught" perimeter and area. #elemmathchat
I always forget that we are all in different time zones. I'm ready for bed and you're still out headed for a school play. lol. I love how we can all connect from all over the country. #elemmathchat
It's fine. I love being pushed to think further. I come across the same issue all the time. Ss think answers make sense but they really don't. I'd have him label the sides based on his explanation and then calculate the area. Then match that to what info was given. #elemmathchat
Yes it is. We have weekly data meetings in which we spend time truly diagnosing student work. It has helped us move the dial this school year, and I can wait to continue next year. #elemmathchat
A lot of folks (many adults included, in our experience) are used to talking about congruent TRIANGLES, not congruent RECTANGLES, and that persists through this problem. So I'm not so worried about it in this context. #ElemMathChat
A7: Lissa's perimeter formula is off a bit. She knew she had to add to find perimeter, however, she is unsure of what info to use to add.
She seems to understand area. I think her writing triangle was a mistake. #elemmathchat
It's neat to me that you want to push Matteo to go to the concepts of perimeter and area -- we know he knows the formulas but not what he understands about the concepts OTOH we don't know he DOESN'T understand the concepts. #elemmathchat
A7: Lissa knows that each of the 7 rectangles will have *something* that is the same about them (dividing 756 by 7), which gives me some evidence she has an emerging understanding of congruence as "the same" #elemmathchat
No it wouldn't. Once he labeled 756 on each side, I would have him multiply 756 x 756 to find area. The area would not be 756. I would probably have him use a calculator since the numbers are so large. #elemmathchat
I am having tweetdeck issues. I was wondering if I was looking at the correct graphic. I was like whoa she decomposed this into triangles in her mind! So much in geometry you do just that! ElemMathChat
Yes very hard for most. But my teachers are getting better. We will continue next year. I have them look at their student work samples and tell what errors they notice students making. Then we develop strategies to support with the various misconceptions. #elemmathchat
Yea! Listening really hard and wanting to understand what they're thinking, instead of noticing that they're not thinking the things you want them to, is a big step in helping them make progress. Definitely growth! #ElemMathChat
But if he uses a calculator and actually types in 756x756, he would not get that. This also leads me to believe that we need to spend some time focusing on what square units really mean. #elemmathchat
I wonder if that is the last step that she felt like she understood what to do w/ the problem & went into survival mode. Do a lot with a bunch of numbers to “show your work” #elemmathchat
Ah, but I'm saying what if he thinks the area is (756 units) x (756 units), as in, we aren't given a number for area, but are actually being told the dimensions of the rectangle? Like he is missing what the notation is telling us (the whole "square units" thing). #ElemMathChat
Yes! Listening to their explanations is key. I think a lot of teachers just assume they know what the student was thinking and we miss a lot of learning opportunities because we don't give Ss a chance to completely explain their thought process. #elemmathchat
Then he clearly doesn't understand the concept of square units. We would need to deviate from this problem and reteach that first, before diving further into this problem. #elemmathchat
I think that's a great point. If we had a way to really know what the Ss are thinking, I think many teachers would be amazing/surprised! We make a lot of assumptions instead. #ElemMathChat
I might give him a rectangle with sides labeled something like 8 units and 7 units and ask him to find the area and see what happens. Does he talk about square units? Does he write it? What if I ask him what the units are? #ElemMathChat
